Final answer:
The carrying value of the bonds at December 31, 2022, is calculated using the effective interest method, considering the bond was issued at a premium and the market rate of interest . The carrying value at the end of 2022, rounded, is $631,927.
Step-by-step explanation:
To determine the carrying value of the bonds at December 31, 2022, we must start with the initial value of the bonds when they were issued and adjust for interest amortization over the two years. Since the bonds were issued at a premium (issued for more than their face value), the effective interest method will amortize this premium over the life of the bonds.
Initially, the bonds were issued for $640,640 which is their carrying value on January 1, 2021. The stated interest rate is 9%, but we need to use the market interest rate of 8% to calculate the amortization of the premium. The actual cash paid in interest annually would be the face value of $616,000 times the stated interest rate of 9%, which equals $55,440.
For each year, we must calculate the interest expense using the market rate. For the first year, this is 8% of the initial carrying amount, which is $640,640 * 8% = $51,251.20. The premium amortization for the year is the difference between the interest paid and the interest expense, which is $55,440 - $51,251.20 = $4,188.80. At the end of the first year, the new carrying value is $640,640 - $4,188.80 = $636,451.20.
In the second year, we calculate interest expense on this new carrying value: $636,451.20 * 8% = $50,916.10. The premium amortization is then $55,440 - $50,916.10 = $4,523.90. The carrying value at the end of the second year, and our final answer, would be $636,451.20 - $4,523.90 = $631,927.30.
Rounding to the nearest whole dollar, the carrying value of the bonds at December 31, 2022, is $631,927.